David Cameron says it is up to parents to protect their children from accessing pornography on the internet, rather than the government making drastic changes to the school curriculum.

The prime minister admitted he was still "grappling" with how to talk to his own children about the dangers of internet porn.

Sex and relationship education in schools must address internet porn, the prime minister said, but he agreed with education secretary Michael Gove that there was no need for "wholesale reform" of the curriculum.

Speaking on Friday, Cameron said: "We need to make sure we are up to date on the problems of the internet.

"Where I absolutely agree with the education secretary is that I am not looking for wholesale reform of the curriculum on sex education. We should be alert to those points and make those changes, but I don't think we need wholesale reform."

On Thursday Gove rejected a call from the deputy prime minister, Nick Clegg, to upgrade sex education guidelines to keep pace with the explosion in internet porn.

Asked whether parents should play their part in educating children about cyber-porn, rather than leaving the issue to teachers, Cameron said: "We have all got to get involved because of the internet. We all have to learn more about the internet, the dangers of the internet, the issue of access for children."

Parents needed to be ready to talk to their children about porn and to educate themselves about the use of parental controls to limit what their children could access, he said.

"This is where sex and relationship education at school can help," he said. "But because so much computer access goes on in the home, I am afraid we are all going to have to get better at understanding all these issues around parental controls.

"We are all going to have to ask ourselves questions about what it is OK for children to access and when. I am grappling with this myself."

The boy addicted to porn; the girl who endured sexual assault to get her BlackBerry back… In Beeban Kidron's sobering documentary British teenagers open up about how they use and feel about their smartphones and the internet

Tim Lott: It's not so much the sex as the fact that it is full of images of hatred and abuse of women. What does it do to young people's understanding of what constitutes a healthy sexual relationship?